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# AD is the longest side of the right triangle ABD shown in the figure.

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
AD is the longest side of the right triangle ABD shown in the figure.  [#permalink]

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Updated on: 15 Jul 2019, 04:14
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:28) correct 20% (02:00) wrong based on 25 sessions

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AD is the longest side of the right triangle ABD shown in the figure. What is the length of longest side of ∆ABC ?

(A) 2
(B) 3
(C) √41
(D) 9
(E) 41

Source: Nova GMAT
Difficulty Level: 550

Attachment:

triangle.jpg [ 29.12 KiB | Viewed 586 times ]

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Originally posted by Bunuel on 09 Oct 2018, 21:39.
Last edited by SajjadAhmad on 15 Jul 2019, 04:14, edited 1 time in total.
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Re: AD is the longest side of the right triangle ABD shown in the figure.  [#permalink]

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10 Oct 2018, 02:28
Bunuel wrote:

AD is the longest side of the right triangle ABD shown in the figure. What is the length of longest side of ∆ABC ?

(A) 2
(B) 3
(C) √41
(D) 9
(E) 41

Attachment:
triangle.jpg

For Ad to be the longest side of right triangle, angle B must be 90º because the side opposite to the biggest angle is biggest

i.e. Ac = Hypotenuse of triangle ABC $$= √(4^2+5^2) = √41$$

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Math Expert
Joined: 02 Aug 2009
Posts: 7940
Re: AD is the longest side of the right triangle ABD shown in the figure.  [#permalink]

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10 Oct 2018, 02:42
Bunuel wrote:

AD is the longest side of the right triangle ABD shown in the figure. What is the length of longest side of ∆ABC ?

(A) 2
(B) 3
(C) √41
(D) 9
(E) 41

Attachment:
triangle.jpg

1. Two ways...
A) geometry..
ABD is a right angled triangle and AD is biggest side so, angle ABD is 90...
∆ABC is also a right angled triangle, so $$AC^2=AB^2+BC^2=4^2+5^2+16+25=41.....AC=√41$$

B) choices ..
Even if ABC was not a right angled triangle, only one choice would have fit in..
Since AC is the longest side and other two are 4 and 5 , $$AC\geq{5}$$
Also AC<AB+BC.....AC<4+5.....AC<9
Only √41 fits in
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Re: AD is the longest side of the right triangle ABD shown in the figure.   [#permalink] 10 Oct 2018, 02:42
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